"Next Generation Science Standards" ("NGSS") three-dimensional learning is valuable for all students regardless of age. The "NGSS" integrate disciplinary core ideas, science and engineering practices, and crosscutting concepts, adding rigor to science teaching and learning. Though "NGSS" performance…

In this study, the design, implementation and evaluation processes of the 4MAT teaching model activity, which is designed in accordance with the holistic brain model for teaching the graphic representation of data at the 8th grade level and making the appropriate transformations between these representations, are presented in this study. The…

This paper explains how an original conceptual framework model for mathematics pedagogy, the Australian Curriculum Conceptual Rubric (ACCR), has continued to be used successfully by the author in pre-service and in-service teacher education programs over the past ten years or more. Now further enhanced by a deeper reflection upon Peter Sullivan's…

Abstract concepts of mathematics are always difficult for the students to comprehend. These concepts are a continuous source of low achievement in mathematics. A study was conducted to explore the effect of Synectics Model of teaching in enhancing understanding of abstract concept of mathematics. It was a form of quasi-experimental study using…

"The root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25". Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives--epistemic and pedagogical--drawing on Toulmin's notion of…

The calculus concepts of concavity and inflection points are often given meaning through the shape or curvature of a graph. However, there appear to be deeper core ideas for these two concepts, though the research literature has yet to give explicit attention to what these core ideas might be or what it might mean to "understand" them.…

Students in grades 3 and 4 attending a traditional public elementary school in a northeastern state did not meet proficiency levels in mathematics as measured by the state's assessment system. Published reports indicated that students attending the Montessori programs were more proficient in solving math problems compared to students in…

This paper discusses the results of a three-year mixed methods study into the effectiveness of a mathematics education unit. This was written for both pre-service primary education students and re-training in-service teachers, to prepare them for the teaching of pre-algebra and early algebra. The unit was taught rom 2013 to 2015 inclusively in a…